SOLUTION: please solve these problems with steps: ___________ ___________ 1. ~(K v A) > (R v W) 2. ~K 3. ~A /∴ R v W ___________ ___________ 1. A v ~(O v M) 2. B > ~(A v ~M)

Algebra ->  Proofs -> SOLUTION: please solve these problems with steps: ___________ ___________ 1. ~(K v A) > (R v W) 2. ~K 3. ~A /∴ R v W ___________ ___________ 1. A v ~(O v M) 2. B > ~(A v ~M)       Log On


   

Question 1204115: please solve these problems with steps:
_______________________
1. ~(K v A) > (R v W)
2. ~K
3. ~A /∴ R v W
_______________________
1. A v ~(O v M)
2. B > ~(A v ~M) /∴ ~B
_______________________
1. (Z + ~A) v (B > Z)
2. ~Z /∴ ~B
_______________________
1. ~A
2. ~Z /∴ ~[(A v Z) + B]

Thank you!!!
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
1. ~(K v A) > (R v W)
2. ~K
3. ~A /∴ R v W

4. ~K + ~A      2,3 Conjunction
5. ~(K v A)     4,  DeMorgan's Law 
6. R v W        1,  Modus ponens


_______________________
 1. A v ~(O v M)
 2. B > ~(A v ~M) /∴ ~B

 3.               |~~B        Assumption for Indirect Proof
 4.               |  B             3, Double negation 
 5.               |~(A v ~M)     2,4, Modus ponens
 6.               |~A + ~~M        5, DeMorgan's Law
 7.               |~A + M          6, Double negation
 8.               |M + ~A          7, Commutation
 9.               |M               8, Simplification
10.               |M v O           9, Addition
11.               |O v M          10, Commutation
12.               |~(O v M) v A    1, Commutation
13.               |~~(O v M)      11, Double negation
14.               |A           12,13, Disjunctive syllogism
15.               |~A              7, Simplification
16.               |A + ~A      14,15, Conjunction 
17. ~B        Lines 3-16 Indirect Proof 

We only do 2.

Edwin